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A lot of controversy surrounds the subject about tank size, often resulting well intentioned but incomplete advice being given.
This often a controversial subject among aquarists, especially well intentioned advanced aquarists, often resulting in confused aquarists (both beginner and even advanced).

One aspect is often missed and that is that although the gallons per fish rule is a good starting point, there is vastly more that goes into this subject (please see the section later in this article about aquarium sizing).
Also it is important to note that there is no denying that the bigger an aquarium you can afford, maintain or have space for the better for many good reasons!
BUT I have kept MANY aquariums under a variety of conditions and monitored them in controlled experiments and often a small aquarium can work for what many might consider over crowded conditions providing there is excellent filtration, cleaning maintenance, circulation, feeding procedures (and quality food), chemistry, etc.

For example you I can state categorically that 10 gallon aquarium with (2) 2 inch goldfish that is well maintained with a hang on the back (power) and a sponge filter will out have vastly better water parameters than a 20 gallon with the same goldfish that is poorly maintained with a corner bubbler filter.

For example, I kept a 60 gallon Feeder Goldfish tank that often had over 500 goldfish at a time in it.
Is this over crowded?
Certainly, however I kept water parameters good by virtue of twice daily water changes, positive ion mineralization (such as calcium that is often ignored), large amounts of filtration. In the case of the aquarium I am speaking of, a larger tower fluidized filter along with a canister filter and air stones, and finally UV Sterilization, which I cannot say enough about.
This of coarse is an extreme example and NOT meant for long term fish keeping, only VERY short term. My point is I have kept similar Feeder tanks without the same procedures, filtration, etc. and the water parameters were NEVER as good.

As a more “Real World” example is all the controlled trials I performed (mostly using goldfish at the Bahooka Restaurant and Coaster Co. of America, which between the two clients I had over 140 aquariums).
Many of the trials involved filters and stocking and measuring the results and I often found better water parameters, and MUCH healthier fish in the smaller tanks that were maintained with the same number of fish as with the tanks that were often more than twice their size.

The difference was much better filtration, correct chemistry including GH & KH, better maintenance, and UV Sterilization.
All of these also have an affect on Aquarium Redox which is a major indicator of tank health as a healthy Redox Balance normally shifts a little between night and day, but an unhealthy Redox balance will often have large swings or have unusually high or low ORP numbers according to a Redox Neter.

I should make one more point as per determining if a tank is too crowded or not (which was noted earlier about twice daily water changes), and that is the water change schedule. In fact if “flow through” water change methods are employed correctly, this can greatly increase the amount of fish the tank can hold (assuming you are not trying to keep a 12 inch arowana in a 20 gallon tanks where other issues then arise). This is possible in part due to improved Redox, mineralization and low hormone levels from the fish since these are removed via the constant changes of water.
See this article:Aquarium Cleaning; Methods

It may seem like I am promoting situations that would induce stunting, but I am NOT.
I am referring to fish populations that can live comfortably within their surroundings and with their tank mates, or in the case of goldfish, knowing that anything less than an 8-10 gallon for short to medium term is not healthy, while a 20 gallon PLUS is much better for the long term.

Stunting would involve placing a baby Arowana or Quetzal Cichlid (or similar cichlid that will easily grow to 12 plus inches) in a 20 gallon aquarium.
Stunting IS CRUEL, and at the very least does not allow the fish to reach its full potential, including lifespan.

There are many theories that go into what happens biologically in stunting, here are a few thoughts:

Often the tanks these fish are in have high nitrates which are converted into nitrites in the bloodstream and weakens the fish.
See this article: "Aquarium Nitrates, about"

Hormones excreted from the fish inhibit growth (and lifespan), which are more concentrated in a tank too small for the fish there in contained.

Picture Examples of potentially over crowded aquariums
Both these pictures are photo-shopped examples, not actual aquariums.

In this photo-shopped example a Quetzal Cichlid (vieja synspila) is shown in a 14 gallon Bio Cube. This fish has NO chance of long term or even short term viability due to its large size, inability to move around, and inability to carry out its natural behaviors.
Honestly this picture needs little explanation.

In this photo-shopped example, we have an aquarium that is a potential short to medium term problem and a definite long term problem.
The difference short term to medium term is filtration and maintenance. This is a viable tank while the goldfish are still young with good filtration/maintenance.

This tank shown has a built in wet/dry and separate Sponge Filter that has the pump directing water out to a 7 watt Terminator UV Sterilizer and back in.
If this tank was stocked with fish such as Platties that have no chance of out growing/stunting, this set up could easily handle a higher what is considered “Normal” number of fish.

Start with as large an aquarium as you can afford and have space for (even for bettas).
The very BASIC principle that is to have 1-2 inches of NARROW bodied fish per FILTERED aquarium gallon is a starting point, but not very accurate.
This also only applies to a standard rectangular aquarium. Goldfish are dirty and fatter, so I would triple this with them, in fact for long term goldfish health, one goldfish per 8 gallons (30 liters) is best for long term health and "grow out".

Obviously longer fish need more tank width and length. I would decrease the amount of fish proportional to the gallons in a tall aquarium or hexagon aquarium.
Remember, many fish purchased can grow much larger than your original purchase size (ex: goldfish), so keep this in mind too.

To figure your tank size get your tank length, height, and width in inches then apply this formula (multiple all dimensions):
L x H x W = X;
Then divide X by 231
This gives you exact gallons of the tank.
In round tanks or unusual shapes you will have to extrapolate.
To convert gallons to liters multiply by 3.785
Example: a 20 gallon tank = 75 liters.

What is much more important in determining how many fish you should add to your aquarium are these factors:

The amount of surface area relative to the gallons of water the aquarium holds.
I have observed many tall narrow aquariums over the years of my maintenance service where the filtration and other factors were equal to comparable sized and stocked rectangular aquariums, that general fish health and longevity were lower.

Type of fish; such as fish that naturally produce more waste (partly due to the type of food they eat) such as goldfish where one fish per 8+ gallons are better, however small goldfish can be kept in a smaller aquarium with the aquarist knowing that this is short term housing.

Fish such as an Arowana that stays primarily on the surface will need a disproportionately large aquarium (I recommend 200 + gallons for just one Arowana). And as pointed out earlier, you cannot compare a heavy bodied cichlid for instance to a narrow bodied tetra of similar length (and again consider what Cichlid will grow to!!)

Filtration & Circulation; a properly filtered aquarium (good bio filtration, good mechanical filtration, and good circulation) with multiple aquarium filters is important.
Good filtration with quality well maintained filters can go a long ways in allowing an otherwise small aquarium to hold more fish.

Maintenance schedule that includes regular efficient water changes. Good cleaning routines (20% water changes with a gravel vacuum once per week or two).
If you have nitrates that struggle to stay below 40-50 ppm, you probably have an over stocked aquarium (especially if there are live plants!).

Also a kH and pH that starts out at proper levels, but then drops quickly after water changes and/or addition of stabilizing chemicals or products such as Wonder Shells can indicate over stocking (as well as other problems such as mulm buildup).
Reference: Aquarium Chemistry

Using “flow through” water changes where by a small amount of water being is constantly being changed can allow for much more stocking if done correctly as this allows for improved Redox and considerably lowers hormones in the water.
See this article in the section about flow through cleanings: Aquarium Cleaning; Methods

Well maintained water chemistry; including GH, KH and Redox not just low ammonia, nitrites, and nitrates. This is an area of aquarium keeping that is often missed even by advanced aquarists since many are not ware of the effect on overcrowding a tank with low electrolytes or an unbalanced Redox have.

New or experienced aquarist; a new aquarist needs to start with a much less crowded aquarium.

Proper feeding; Over feeding and/or feeding a poor diet that is mostly passed through the fish’ digestive tract due to low digestibility is a major cause of pollution, leading to high DOC, high nitrates, unstable pH, and poor Redox Balance.
All of which will make an otherwise un-crowded aquarium become overloaded as per bio load and capacity.
Further Reference: Bio Load in Aquarium or Pond

Even UV Sterilization will improve bio load as it improves Redox balance and immunity as well as simply lowering DOC (Dissolved organic compounds.

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